This is pretty much a question for the astronomy fen on the board, but it’s been a niggling question for years now for me:
How close would the following objects have to be to be visible with the naked eye (assume 20:20 vision and good but not ideal viewing conditions)?
a Ceres-size asteroid
a “brown dwarf”
a white dwarf
a planet of another star – how close would the system have to be; you can assume any characteristics for star and planet(s) that you choose
a satellite of another planet (how close the planet-satellite system would have to be, and assume whatever characteristics suit you for the characteristics of planet and satellite)
a terrestrial planet, to show a discernible disk
a supergiant (this is more a question of how far away a supergiant could be and still be visible to the naked eye)
The furthest visible supergiants that are discernable as individual stars are about 9000-10000 light years away. Of course, you can see much more remote things with the naked eye that are made up of stars - the Andromeda Galaxy is 2.5 million ly away - but to see one individual supergiant star as a single star, 10000 ly is about the limit. You cannot see any star in the sky more distant than that.
For a terrestrial planet, I would point out that under very good conditions, someone with 20/20 vision can see that Venus is a disk when it’s close to Earth. That’s what, 45 million miles?
I believe Venus is about 20,000,000 miles away when it’s at its closest to earth, but still visible.
A planet of another star - well, the limit for a gas giant is somewhere between Saturn and Uranus, size- and distance-wise. That’s about how close you’d have to be.
Vesta, with a diameter of 500 km, is brighter than Ceres (913 km diam).
Vesta will be at opposition Mar. 31, 2003 and have a magnitude of 5.9. That’s right at the limit of naked eye visibility. Vesta’s orbits between 2.15 and 2.17 AU from the sun, so its closest aproach to earth will be about 1.15 AU. Ceres is further out at between 2.55 and 2.98 AU. More asteroid magnitudes
I’m taking the privilege of bumping this thread once, since I was hoping for responses from The Bad Astronomer, Podkayne, or another informed astro-buff, and they apparently didn’t see the thread before it dropped off the face of GQ.
For “satellite of another planet”, the question is a bit more complicated. For instance: The Galilean moons of Jupiter (Io, Europa, Ganymede, Callisto) are all bright enough to be seen fairly easily by the naked eye, except that they’re too close to Jupiter, and get lost in the glare. We can’t see the moons of Mars with the naked eye, because they’re so tiny, but a person on Mars would be able to see our own huge Luna with the naked eye. And for all of your non-star objects, how much light they’ll be giving off depends on how close they are to their parent star, and how reflective their surfaces are.
I think it’s best to answer your question using some general rules. First, it is generally accepted that the limit for the unaided human eye to detect a heavenly body is an object of 6th magnitude…which is quite dim Therefore…
To answer your question more exactly, there are formulas (of which I am only vaguely familiar) which relate size and distance to magnitude. Speaking in general terms, each celestial object for which you inquire does not have one standard diameter nor some pre-defined diameter. In brief, the greater diameter you pick, the greater distance by which said object would be visible. In short, using such formulas, fix the magnitude to 6. Then, play with other variables as you wish to find various answers to your questions.
It may help for you to know that the red giant, Betelgeuse, within Orion is only about 1200 light years away. Hope this gives you some food for thought. - Jinx
The brightness of a star is usually given in units of absolute magnitude. The absolute magnitude of a star is simply a measure of how bright a particular star would appear in the sky if it were at a standard distance of 10 parsec or 32.6 L.Y.
Here’s a table of absolute magnitudes for various types of stars:
Main Sequence stars
Sp M_vis
O5 -5.8
B0 -4.1
A0 +0.7
F0 +2.6
G0 +4.4
K0 +5.9
M0 +9.0
M5 +11.8
M8 +16
Supergiants -5 to -7
Giants 0 to -5
White Dwarf 6 to 14
Substellar Brown Dwarf 17 and up
(From a Hertzsprung Russell diagram like this.)
The magnitude at any other distance can be calcalculated with the formula m = M + 5log(d) - 5 ( M = absolute magnitude, d is in parsecs)
For the limit of visibility, mag 6, that works out to 6 = M + 5log(d) - 5
After algebra: d = 10^((11 -M)/5) where d is now the distance at which the star will be just barely visible to the naked eye.
The table below gives that distance for stars of different absolute magnitudes.
Absolute magnitude for asteroids are defined as the brightness at 1 AU from earth and 1 AU from the sun. 1 parsec = 206,265 AU. Moving a Abs magnitude 3 asteroid into a 1 AU orbit about a sunlike star 1 parsec away would decrease its brightness by a factor of 2.35E11 (206,265^2). That would give it a magnitude of 29.7. (assuming I did the math right).
Planets about other stars could be given the same treatment, but you can already see that they make extremely dim companion objects.